The high throughput detection of small molecule inhibitors and/or enhancers of particle interaction is desired in many fields of science. By “particle,” we refer to such objects as protein and polymer molecules together with their conjugates and co-polymers, viruses, bacteria, virus-like particles, liposomes, polystyrene latex emulsions, nanoparticles, and all such particles within the approximate size range of one to a few thousand nanometers. Dynamic light scattering provides an excellent analysis method for screening large chemical libraries, such as small molecule libraries of compounds, for effectors of particle interactions. Such libraries are typically available at molecular screening centers, such as the Scripps Research Institute Molecular Screening Center in Jupiter, Fla., the Broad Institute in Cambridge, Mass., the Molecular Screening Shared Resource centered at the University of California, Los Angeles, and others. Small molecule libraries of compounds may also be held by companies, private individuals, foundations, etc. Compound collections can exceed 300,000 molecules that possess diverse architecture and function. Depending on the particles used, the high throughput screening of chemical libraries can lead to a greater understanding of cellular function, the discovery of new drugs, or any variety of nanotechnology-related innovations.
Additionally, libraries of macromolecules, such as a library of a proteins subjected to site directed mutagenesis at a large number of sites, may also be screened to identify which residue(s) modulate/change interactions with the binding partner(s). Additionally libraries of nanoparticles, such as gold particles or quantum dots, may also be screened against binding partners using this method. Alternatively, a nucleic acid fragment library could be screened against a protein to determine which region the protein may bind to. The aforementioned screen types could be done in the presence or absence of small molecule modulators. Any particle type can potentially be screened in this manner.
The detection and characterization of reversible associations of particles in solution is also essential in many areas of science. For illustrative purposes, we shall focus specifically upon the interactions of protein molecules and their conjugates, though the techniques disclosed will be equally applicable to all the other particle types listed. Whenever the word “molecule” is used within this specification, it will be understood that the word “particle” may be substituted therefore in most cases without any limitations implied upon the inventive methods described. The study and measurement of molecular associations is important for many reasons; whether to gain understanding of cellular function or to develop and formulate pharmaceuticals or other biologically active materials. Essentially, most pharmaceuticals have functionality due solely to association with molecules within the body, so the discovery and accurate characterization of these associations is a key element for pharmaceutical development.
Molecules of the same species may self-associate to form dimers, trimers, and higher order complexes, whereas molecules of different species may associate with each other to yield complexes of various compositions. More than two particle types may combine to form a complex. Such associations may be reversible or irreversible. For reversible associations, the binding affinities are characterized by a unique equilibrium constant. The equilibrium constant specifies the relative concentrations of the complex(s) and the component monomers for a given set of conditions. According to Le Châtlier's principle, every closed system must eventually reach equilibrium. When reactants in a reversible process are in excess of their equilibrium concentrations, the reaction proceeds to convert the reactants to products and achieve equilibrium. Alternately, when products are in excess, the reaction proceeds in a reverse direction to convert product to reactant and again achieve equilibrium. For the reaction of molecules A and B to form the complex AB, A+BAB, the equilibrium association constant is written:
            K      a        =                  [        AB        ]                              [          A          ]                ⁡                  [          B          ]                      ,where the bracketed terms correspond to the corresponding concentrations of the molecules A, B, and their complex AB. Although constant under stable conditions, the equilibrium constant of a given association may change in response to environmental factors, such as temperature, buffer salinity, or the presence of other factors modulating the interaction.
There are many techniques used to measure equilibrium constants and characterize molecular associations. However, the majority can detect only tightly bound interactions, and require the tagging/labeling or immobilization of one of the binding partners. As any modification of the molecule can potentially influence the interaction, techniques implementing free-solution testing are optimal. “Free-solution” means that molecules are neither tagged/labeled nor immobilized for analysis. As no molecule-specific immobilization/tagging protocol is required, free solution techniques are not limited to a single molecular type, such as proteins. Free solution techniques are applicable to most molecular types.
There are several well-established free-solution methods to determine stoichiometry and equilibrium constants, such as calorimetry and sedimentation equilibrium. Static light scattering is another option. The theory of using static light scattering measurements at different solution concentrations to determine self or hetero association constants has long been known, cf. Huglin, 1972 Light Scattering From Polymer Solutions, Academic Press, London and New York, by W. Burchard and J. M. G. Cowie in Section 17, Selected Topics in Biopolymeric Systems, as well as Hirs, 1973, Methods in Enzymology Volume XXVII, Enzyme Structure, Part D, Academic Press, London and New York, by Pittz et al. in section 10, Light Scattering and Differential Refractometry. Such measurements were demonstrated fairly recently by T. Yamaguchi et al. in Biochem. Biophys. Res. Commun., 2002, Vol. 290, 1382-1387 and improved upon by Attri et al., in Anal. Biochem., 2005, Vol. 346, 132-138, where they termed the technique “concentration gradient light scattering”.
In static light scattering, the intensity of scattered light is proportional to the molar mass of the molecule; a dimer scatters twice as much light as two monomers. For example, in the study of self-association, the static light scattering concentration gradient method measures the intensity of scattered light over a series of concentrations of the molecule studied. The scattered light changes for each concentration, in accordance with the change in the population of the associated species. The association constant quantifies how the associated species change at different concentration ratios. To determine the association constant and stoichiometry of the interaction, the experimental data are fit against models that estimate the concentrations of the individual components present at each solution concentration.
The three free-solution methods, static light scattering, calorimetry, and sedimentation equilibrium, require a relatively large amount of sample when used in their standard configurations. Techniques requiring minimal sample quantities for measurement are often required, as the required molecules may not be available in sufficient quantities, as synthesis or isolation and purification can present significant challenge and expense. Finally, none of the three methods are suitable for high-throughput measurement. Thus, the low productivity characteristics of all three methods impede practical study spanning a large compositional range.
Recently, a fourth free-solution method has been explored: back-scattering interferometry with high-throughput capability and very low sample requirements. Cf Bornhop et al. Science 317, pages 1732-1736 (2007). Unfortunately, this method is limited to systems that bind in a 1:1 ratio. Other stoichiometries, which commonly occur in nature, cannot be distinguished or characterized.
The search for a free-solution, high-throughput method with low sample requirements and the ability to detect multiple binding stoichiometries remains. To date, no such method has been reported. Our inventive method, on the other hand, based on the use of dynamic light scattering resolves, thereby, the previously discussed problems.
Dynamic light scattering is a well-established technique, typically used to determine the diffusion coefficients of scattering particles in solution and, from them, an associated set of hydrodynamic radii. The hydrodynamic radius is the radius of a hard sphere whose diffusion coefficient is the same as that measured for the sample particle. Dynamic light scattering, also known as quasi-elastic light scattering, or QELS, uses the measured fluctuations in the light scattered from a sample to determine these quantities. When in solution, sample particles are buffeted by the solvent molecules. This leads to a random motion of the particles called Brownian motion. As light scatters from the moving particles, this random motion imparts a randomness to the phase of the scattered light, such that when the scattered light from two or more particles is combined, a changing intensity of such scattered light due to interference effects will occur. The dynamic light scattering measurement of the time-dependent fluctuations in the scattered light is achieved by a fast photon counter. The fluctuations are directly related to the rate of diffusion of the particles through the solvent. The fluctuations are then analyzed to yield diffusion coefficients and, from these, the hydrodynamic radii of the sample.
The time variations of the intensity fluctuations are quantified by means of so-called autocorrelation techniques. Depending upon the experimental configuration of the dynamic light scattering instrumentation, the resulting autocorrelation function may be an intensity-intensity or field-field autocorrelation function, or a combination of these two. The intensity-intensity correlation function is
                                          g                          (              2              )                                ⁡                      (            τ            )                          =                              〈                                          I                ⁡                                  (                  t                  )                                            ⁢                              I                ⁡                                  (                                      t                    +                    τ                                    )                                                      〉                                              〈                              I                ⁡                                  (                  t                  )                                            〉                        2                                              (        1        )            where I(t) is the intensity of the scattered light at time t, and the brackets indicate averaging over all t. The correlation function depends on the delay τ, that is, how the intensity variation in time t+τ correlates to the intensity variation in t. FIG. 1 shows a typical correlation function for a sample of Immunoglobulin G protein in solution. In this figure open triangles are data, and the solid line is a fit of the data to a simple exponential function, described below.
As described in various light scattering texts, cf. B. Chu, Laser Light Scattering: Basic Principles and Practice, (Academic Press, Boston, 1991), for a single particle freely diffusing in solution, the correlation function of Eq. 1 becomesg(2)(τ)=B+β exp(−2Γτ)  (2)where B is the baseline of the correlation function at infinite delay (τ→∞), β is the correlation function amplitude at zero delay (τ=0), and Γ is the decay rate.
An algorithm is used to fit the measured correlation function to Eq. (2) to retrieve Γ. From this point, the diffusion coefficient for the particle, D, is calculated from Γ from the relation,
  D  =            Γ              q        2              .  Here, q is the magnitude of the scattering vector, i.e.
      q    =                            4          ⁢          π          ⁢                                          ⁢                      n            0                                    λ          0                    ⁢              sin        ⁡                  (                      θ            /            2                    )                      ,where n0 is the solvent index of refraction, λ0 is the vacuum wavelength of the incident light, and θ is the scattering angle. Finally, the hydrodynamic radius rh of an equivalent diffusing sphere is derived from the Stokes-Einstein equation,
            r      h        =                            k          B                ⁢        T                    6        ⁢        π        ⁢                                  ⁢        η        ⁢                                  ⁢        D              ,where kB is the Boltzmann constant, T is the absolute temperature, and η is the solvent viscosity.
Since it is relatively insensitive to stray background light from the walls of the containing structures, dynamic light scattering measurements may be made from very small sample volumes, thus reducing sample quantity requirements and enabling the use of high throughput measurements. As such, dynamic light scattering may be used with microtiter plate based systems or very small volume cuvettes, each such sample holding element containing only a few microliters of sample. Although such measurements require a higher concentration of sample relative to those needed for static light scattering measurements, the smaller sample volumes typically result in a significant overall reduction in total sample quantity required.
The application of the static light scattering concentration gradient procedures to dynamic light scattering, DLS, would be a significant improvement for determining particle association stoichiometry and affinity, as this would permit far smaller sample quantities, as well as high throughput processing. For the static light scattering method, as each different sample composition is examined, an associated excess Rayleigh ratio is measured. Such Rayleigh ratios are related directly to the molecular species producing them. A dynamic light scattering measurement, on the other hand, yields a correlation function derived from the scattered light fluctuations attributed to these same molecular species. Such correlation functions may be decomposed, following certain assumptions, to represent the distributions, in terms of diffusion coefficients and their associated hydrodynamic radii, of the scattering molecules.
Whereas static light scattering data are relatively easy to model in terms of postulated associated states, DLS responses to the presence of such states are far more complex. For example, the molar mass of a molecular homodimer scatters four times the amount of light as one of its two monomers, or twice as much light as scattered by the two separated monomers. On the other hand, the difference of the diffusion coefficient of a dimer from that of one of its composite monomers depends critically upon the structure of the associated dimer. Considering just the corresponding hydrodynamic radii as a measure of these differences, there may be a range of values, whereas for the static light scattering case there is a known discrete value.
The application of dynamic light scattering, for obtaining molecular association constants and stoichiometries by modeling thereof a series of relative concentration gradients has been attempted infrequently over the past four decades, although DLS techniques are frequently used to study irreversible particle association, particularly particle aggregation. Examples of such prior work are described by Claes, et al. in Chapter 5, An on-line dynamic light scattering instrument for macromolecular characterization, of Laser Light Scattering in Biochemistry Eds. S. E. Harding, et. al., 1992, The Royal Society of Chemistry, Cambridge, UK, and Wilson Journal of Structural Biology 142, 56-65 (2003).
Self association was studied by Mullen et al., J. Mol. Biol. 1996, 262, 746-755, MacColl et al., Biochemistry 1998, 37, 417-423, an Lunelli, Physical Review Letters 1993, 70(4), 513-516. In the dynamic light scattering industry, Protein Solutions developed a “Fraction Calculator” in an early version of the Dynamics software to determine the fraction of each species in a binary equilibrium, using the average rh and postulating or measuring the two end points. Malvern also has recently published an application note that proposes how the percent monomer in a monomer/dimer system can be estimated using the hydrodymic radius of the mixture.
In terms of heteroassociations, Vannini et al., J. Biol. Chem., 2004, Vol. 279, Issue 23, 24291-24296, used dynamic light scattering to predict the stoichiometry of a protein complex by isolating the complex and estimating the molecular mass of the complex from the hydrodynamic radius. This study involved a complex that could be isolated from the component protein monomers, indicating the association was irreversible or very tightly bound. DLS measurements have also been performed at a series of two or more ratios of two components such as the work by Wang et al., Biopolymers, 1981, v.20, p 155-168, Murphy et al., Biophysical Journal, 1988, 54, 45-56, Leliveld S. R. et al., Nucleic Acids Research, 2003, Vol. 31, No. 16, 4805-4813, and Sharma et al., Biophysical Journal: Biophysical Letters, 2008, L71-L73.